RENTON, Wash. — Shaquem Griffin became an NFL star the moment Seattle selected him in the fifth round of last year’s draft.

The first one-handed player drafted into the league, Griffin and his twin brother Shaquill were NFL darlings. Their story spread across the world, a heartwarming tale of brotherhood, perseverance and overcoming adversity. Fame came swiftly, as did media inquiries and endorsement contracts.

In the same round of that same draft, Seattle selected punter Michael Dickson and defensive back Tre Flowers. Their selections received far less attention, though Dickson slowly developed into a fan favorite during offseason training because of the wizardry he performs when kicking a football.

By Week 1 of the regular season, all three fifth-rounders were in Seattle’s starting lineup. Dickson had done enough to force the release of veteran Jon Ryan, Flowers had climbed the depth chart thanks to injuries to Byron Maxwell and Dontae...